st: Fixed effect regression with and without state fixed effects

Dear statalist,
I have a question on panel fixed effect regression.
I have a balanced panel from 2000-2009 on 51 states. The variable I am
interested in is x1.
x2-x4 are control variables and are largely state specific. When I ran
the following command
xtreg Y x1 x2 x3 x4, fe
it returned a significant negative sign for the coefficient. However,
the sign I was expecting was positive.
I did the same regression without the state fixed effect using OLS and
year dummies as follows.
reg y x1 x2 x3 x4 i.year
this regression returned a positive (as expected) and significant sign
for the coefficient of x1 while the signs and significance of other
variables in the model remained the same. Now I am wondering which
model to go with.
I did a lrtest between both the models. For this purpose the xtreg
model was estimated as
reg y x1 x2 x3 x4 i.year i.state
The lrtest choose the model with both state and time fixed effect.
Obviously adding about 51 state dummies will certainly increase the
overall fit of the model and return higher F stats and R squares. Is
there anything else I need to do to ensure the correct specification?
The Hausman test favored a fixed effect model over a random effect model.
As per the literature I am more comfortable with a positive sign of
the x1 variable which is obtained by removing state fixed effects.
Any help will be appreciated.
Thanks,
Rijo.
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